TLS MODELLING OF ANISOTROPY IN MACROMOLECULAR

REFINEMENT

Martyn Winn

CCP4, Daresbury Laboratory, U.K.

York, April 11th 2002

Aims• Mean square atomic displacements (static and

dynamic) are an important part of model of protein.

• Atomic displacements are likely anisotropic, but rarely have luxury of refining individual anisotropic Us. Instead isotropic Bs.

• Intermediate descriptions??

Contributions to atomic U U = Ucrystal + UTLS + Uinternal + Uatom

Ucrystal : overall anisotropic scale factor w.r.t. crystal axes.

UTLS : rigid body displacements e.g. of molecules, domains, secondary structure elements, side groups, etc.

Uinternal : internal displacements of molecules, e.g. normal modes of vibration, torsions, etc.

Uatom : anisotropy of individual atoms

Rigid body model

Rigid body motion

General displacement of atom (position r w.r.t. origin O) in rigid body:

u = t + D.r

For small libration :

u t + r

TLS parameters• Corresponding dyad:

uu = tt + t r - r t - r r

• Average over dynamic motion and static disorder gives atomic anisotropic displacement parameter (ADP):

UTLS <uu> = T + ST r - r S - r L r

• T, L and S describe mean square translation and libration of rigid body and their correlation.

• T 6 parameters, L 6 parameters, S 8 parameters

Use of TLS

UTLS <uu> = T + ST r - r S - r L r

• Given refined U’s, fit TLS parameters

- analysis

• Use TLS as refinement parameters

TLS U’s structure factor

- refinement

TLS in refinement

• TLS parameters are contribution to displacement parameters of model

• Can specify 1 or more TLS groups to describe contents of asymmetric unit (or part thereof)

• 6 + 6 + 8 = 20 parameters per group (trace of S is undetermined)

• Number of extra refinement parameters depends on how many groups used!

At what resolution can I use TLS?

• Resolution < 1.2 Å - full anisotropic refinement

• Resolution ~ 1.5 Å - marginal for full anisotropic refinement. But can do detailed TLS, e.g. Howlin et al, Ribonuclease A, 1.45 Å, 45 side chain groups; Harris et al, papain, 1.6Å, 69 side chain groups.

• Resolution 1.5 Å - 2.5 Å model molecules/domains rather than side chains.

• Sandalova et al 2001 - thioredoxin reductase at 3.0 Å - TLS group for each of 6 monomers in asu

Implementation in REFMAC

Suggested procedure:• Choose TLS groups (currently via TLSIN file). • Use anisotropic scaling.• Set B values to constant value.• Refine TLS parameters (and scaling parameters)

against ML residual.• Refine coordinates and residual B factors.

NCS

• Different molecules in asymmetric unit may have different overall thermal parameters.

• Refine independent overall TLS tensors for each molecule.

• REFMAC can then apply NCS restraints to residual B values of NCS-related molecules.

TLSINTLS Chain O NAD bindingRANGE 'O 1.' 'O 137.' ALL RANGE 'O 303.' 'O 340.' ALL

TLS Chain O CatalyticRANGE 'O 138.' 'O 302.' ALL

TLS Chain Q NAD bindingRANGE 'Q 1.' 'Q 137.' ALL RANGE 'Q 303.' 'Q 340.' ALL

TLS Chain Q CatalyticRANGE 'Q 138.' 'Q 302.' ALL

Choice of TLS groups

• chemical knowledge, e.g. aromatic side groups of amino acids, secondary structure elements, domains, molecules

• best fit of TLS to ADPs of test structure, e.g. Holbrook & Kim (1984); rigid-body criterion applied to ADPs, e.g. Schneider (1996)

• dynamic domains identified from multiple configurations, e.g. more than one crystal form (DYNDOM), difference distance matrices (ESCET), MD simulations.

TLS - refmac5 interface

•Select TLS & restrained refinement at top of interface•Specify TLS in and TLS out files.•TLS Parameters folder:

•Number of cycles, e.g. 20•Fix Bfactors to e.g. 20 (value not crucial, but option is

recommended)

What to look for in output

•Usual refinement statistics.

•Check R_free and TLS parameters in log file for convergence.

•Check TLS parameters to see if any dominant displacements.

•Pass XYZOUT and TLSOUT through TLSANL for analysis

•Consider alternative choices of TLS groups

TLSOUT

TLS Chain O NAD bindingRANGE 'O 1.' 'O 137.' ALLRANGE 'O 303.' 'O 340.' ALLORIGIN 94.142 6.943 75.932T 0.5200 0.5278 0.5031 -0.0049 -0.0040 0.0081L 0.11 0.08 0.04 -0.03 0.02 0.06S -0.014 0.020 0.002 0.022 0.000 -0.016 -0.005 0.022

.

.

.

Equivalent isotropic B factors

• TLS tensors UTLS for atoms in group.

• UTLS BTLS and anisotropy A

• Also have individually refined Bres

• Hence, BTOT = BTLS + Bres

Running TLSANL

XYZIN: output coordinates from refmac with residual B factors (BRESID keyword)

TLSIN: output TLS parameters from refmac

TLSIN: ANISOU records including TLS and residual B contributions

ATOM records containing choice of B (ISOOUT keyword)

AXES: If AXES keyword set, file of principal axes in molscript format

Output of TLSANLOrigins (T and S, but not L, origin-dependent):• Origin of calculation

• Centre of Reaction

Axial systems for each tensor:• orthogonal

• librational

“Simplest” description:3 non-intersecting screw axes + 3 reduced translations

Displaying derived ADPsORTEP: http://www.ornl.gov/ortep/ortep.html

Mapview: http://www.chem.gla.ac.uk/~paule/chart/

xtalview: http://www.scripps.edu/pub/dem-web/toc.html

Rastep in RASTER3D : using the script: grep NAD file.pdb | rastep -auto -Bcol 5. 35. > ellipsoids.r3d render -jpeg < ellipsoids.r3d > ellipsoids.jpeg

Xfit: http://www.ansto.gov.au/natfac/asrp7_xfit.html

povscript: http://people.brandeis.edu/~fenn/povscript

11 a.a. (8% of TLS group)

30% probability level

Ex. 1 - mannitol dehydrogenase

Hörer et al., J.Biol.Chem. 276, 27555 (2001)

1.5 Å data

3 tetramers in a.s.u.

TLS refinement with 1 group per monomer

Free-R 23.6% 20.9%

Tetramer B’s before TLS B’s after TLS crystal contacts

ABCD 27.1 13.3 38

EFGH 18.0 13.3 50

IJKL 18.6 13.3 49

Ex. 2 - light harvesting complex

Complex is nonamer. Each monomer contains: peptide

peptide

2 x B850 bacteriochlorophyll

1 x B800 bacteriochlorophyll

2 x carotenoids

Crystallographic asu = 3 monomers

TLS models

a) 1 group for a.s.u. (20 parameters)

b) 1 group per NCS unit (3 x 20 pars)

c) 1 group per molecule (18 x 20 pars)

d) 3 groups per peptide

+ 1 group per pigment

(total 30 x 20 parameters)

Ex. 3 - peptide-MHC complexes

Markus Rudolph

Class I peptide-MHC complexes (1.7 Å – 1.9 Å)

Alpha chain – 1 or 2 TLS groups

Beta chain – 1 TLS group

Bound peptide – 1 TLS group

Free R decrease 22.3 to 21.1 in best case.

Eigenvalues of L for peptide:

64.7 0.9 -4.1

Example 4 - GAPDH

• Glyceraldehyde-3-phosphate dehydrogenase from Sulfolobus solfataricus (M.N.Isupov et al, JMB, 291, 651 (1999))

• 340 amino acids• 2 chains in asymmetric unit (O and Q), each

molecule has NAD-binding and catalytic domains.

• P41212, data to 2.05Å

GAPDH: R factors

Model TLS groups R factor Rfree

1 0 23.8 30.4

2 1* 25.1 29.4

3 1 21.4 25.9

4 2 21.2 26.2

5 4 21.1 25.8

* B factors constant at 20 Å2

TLS values - 1 TLS group

Eigenvalues of reduced translation tensor:

0.267 Å2

0.112 Å2

–0.005 Å2

Eigenvalues and pitches of screw axes:

1.403 ()2 0.888Å

1.014 ()2 1.472Å

0.204 ()2 1.214Å

Screw axes - 1 TLS group

Contributions to equivalent isotropic B factor

B’s from NCS-related chains

Correlations between NCS-related B's

Model TLS groups R factor Rfree CorrCoeff

1 0 23.8 30.4 0.537

2 1* 25.1 29.4 -

3 1 21.4 25.9 0.752

4 2 21.2 26.2 0.812

5 4 21.1 25.8 0.821

CorrCoeff - mean correlation coefficient between (residual) B factors of NCS-related chains

Application of NCS restraints

Model TLS groups NCS R factor Rfree

CorrCoeff

1 0 no 23.8 30.4 0.537

6 0 yes 25.0 30.3 0.989

5 4 no 21.1 25.8 0.821

7 4 yes 22.0 25.7 0.999

NCS - whether NCS restraints applied

Example 5: GerE

• transcription regulator from Bacillus subtilis (Ducros et al).

• 74 amino acids• six chains A-F in asymmetric unit• C2, data to 2.05Å

GerE

GerE: R factors

Model TLS groups R factor Rfree

1 0 21.9 29.3

2 6 21.3 27.1

Contributions to equivalent isotropic B factor

B’s from NCS-related chains

GerE: NCS

Model TLS groups NCS R factor Rfree CorrCoeff

1 0 no 21.9 29.3 0.519

3 0 yes 22.5 30.0 0.553

2 6 no 21.3 27.1 0.510

4 6 yes 21.4 27.2 0.816

NCS - whether NCS restraints applied

CorrCoeff - mean correlation coefficient between (residual) B factors of NCS-related chains

Choice of TLS groups

6 groups - each group split between 2 chains

(for illustration only!)

Model TLS groups R factor Rfree

1 0 22.5 30.0

2 6 21.4 27.2

5 6 22.2 28.6

Choice of TLS groups

Choice of TLS groups

Inclusion of bound waters

6 TLS groups, with some waters included,

Waters R factor Rfree

None 21.4 27.2

1 shell, cutoff 2.8 21.5 27.4

1 shell, cutoff 3.2 21.5 27.2

2 shell, cutoff 3.2 21.6 27.2

Acknowledgements• BBSRC (CCP4 grant)• Garib Murshudov• Miroslav Papiz (LH2)• Stefan Hörer (mannitol dehydrogenase)• Markus Rudolph (MHC)• Misha Isupov (GAPDH)• Valerie Ducros, Jim Brannigan, Tony Wilkinson

(GerE)